New York’s arm of the Department of Homeland Security is so understaffed it interviews only about 40 percent of foreign-born inmates at Rikers Island – a failure that puts criminal aliens back on the streets instead of deporting them, an internal report says.

The New York field office has the most staff vacancies nationwide, with only 59 percent of approved positions filled, says a report sent to the department’s inspector general in August.

The report, obtained by The Post, accuses department headquarters in Washington, D.C., of “gross mismanagement” and wasting tens of millions of taxpayer dollars.

The understaffing has hampered the agency’s ability to detect and remove offenders from local and state jails and prisons – “hence criminal aliens being released onto the streets of New York,” says the report, which was written by the former district director of detention and removal operations, Edward McElroy.

The report underscores a long-festering public-safety problem.

* Last October, department officials finally rounded up more than 50 foreign nationals in New York and New Jersey that had evaded deportation for years after committing horrific sex crimes on children.

Many of the predators – among 1,300 nationwide – had “escaped through the system,” DHS Undersecretary Asa Hutchinson admitted.

* Another shocking crime rocked New York in December 2002, when several criminal aliens, who had passed in and out of Rikers and other jails without being detected by immigration officials, brutally beat and gang-raped a Queens mother of two near Shea Stadium.

Three of the five rapists were illegal Mexican aliens with multiple prior arrests for crimes including assault, weapon possession and armed robbery.

The problem is twofold, experts say: Cops sometimes do not notify U.S. immigration officers about the arrests; and immigration officers sometimes fail to identify the aliens before they are released on bail or serve out their sentences, said officials of the House Judiciary Committee last year.

Rikers admits an average of 160 foreign-born inmates each week, according to a memo by a U.S. Immigration and Customs Enforcement deportation supervisor.

The memo, dated last March, said the staff of deportation officers at Rikers had dropped from six to four, and they were able to interview only about 42 percent of the inmates.

McElroy’s report says the chronic understaffing also has resulted in a loss of about $23 million since 2002, because the agency doesn’t have the personnel to collect the cash forfeited by aliens who jump bail.

The understaffing also has prevented the full reopening of the agency’s lower Manhattan detention facility on Varick Street, which was evacuated after 9/11.

The agency spent $3 million to renovate the center, and also pays about $1 million a year in rent.

But the 250 beds remain unused, forcing the agency to transport alien detainees picked up in New York to New Jersey jails and federal detention centers in Louisiana, Florida and elsewhere.

The cost of bed space in those facilities runs more than $10 million a year.

McElroy submitted his report after being removed as detention and removal manager in August. He is now a liaison to foreign consuls general.

Marc Raimondi, a DHS spokesman, said the agency is trying to target the most dangerous criminal aliens.

He said the Varick Street center is still useful as a processing facility and workplace for 70 employees and that its status is under review. (p. 9 Metro, Sports)

In trouble

Problems caused by understaffing of Homeland Security’s Detention and Removal operations in New York:

* 42 percent of foreign-born inmates at Rikers Island jail interviewed, putting those who should be deported back on streets.

* 250 beds at high-rent Varick Street detention center cannot be used, forcing agency to spend $10 million a year to house detainees in other states.